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The origin of energy functional in Roothaan open shell SCF theory
Author(s) -
Klimko G. T.,
Mestechkin M. M.,
Plakhutin B. N.,
Zhidomirov G. M.,
Evarestov R. A.
Publication year - 1990
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560370104
Subject(s) - degenerate energy levels , open shell , basis (linear algebra) , basis set , symmetry (geometry) , tetragonal crystal system , energy (signal processing) , molecular orbital , atomic orbital , computational chemistry , coupling (piping) , physics , density functional theory , chemistry , theoretical physics , quantum mechanics , molecule , materials science , mathematics , geometry , phase (matter) , electron , metallurgy
Different methods of averaging of energy over the states of electronic configurations γ N ( n γ = 1, 2, 3 and N = 1, 2, …, 2 n γ − 1) leading to Roothaan' energy expression are considered. The consequent values of vector coupling coefficients ( VCC ) in energy functionals for various states as well as for average values of energy are presented. It is shown also that in molecular systems of cubic and tetragonal symmetry having electronic configurations t N ( N = 2–4) and e 2 there exist states for which VCC are dependent on the choice of basis set of degenerate open‐shell molecular orbitals. The origin of such “non‐Roothaan” terms and peculiarities of its calculation by the restricted Hartree–Fock method are discussed.